Let's call the length of the third edge "Y" so we have edges of 7cm, 5cm and Ycm.There are 6 faces but opposite faces are the same, so there are 3 pairs of faces which are 5cm by 7cm, 5cm by Ycm and 7 by Ycm.The total surface area is therefore 7x5x2 + 7xYx2 + 5xYx2 = 142.
70 + 14Y + 10Y = 142(collect all the Ys)70 + 24Y = 142(subtract 70 from both sides)24Y = 72(divide by 24)Y = 3.
The larger cuboid's smallest edge is 12cm compared with 3cm for the smaller cuboid.The length scale factor will be 12 divided by 3 = 4.The other edges of the cuboid will be 4 x length, so we have edges 4 x 5 = 20cm and 4 x 7 = 28cm.Volume = length x width x height = 12 x 20 x 28 = 6720 centimetres cubed.